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Comment by westoncb | Hacker News Reader

Anyone know of (or want to give) a clear explanation of how gyros behave? I found the article to be unclear on a number of points.

I was also unclear on this: "The first triumph of general relativity was its exact prediction of the orbital precession of Mercury’s perihelion" —does a perihelion precess? I thought it was the planet which was precessing and the perihelion shifted (changing the shape of the planet's orbit?)

Also, I came across this (seemingly) related gem the other day: ("Why is Linear Motion Relative but Rotation Absolute?") https://www.quora.com/Why-is-linear-motion-relative-but-rota...

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Gyros are really simple! Think of the gyro's ring as a series of independent particles flying around really fast in a horizontal circle. Now you push up at one point on that circle. Does the circle move up at that point? No. You're applying a force to each particle only very briefly before it moves past and you're pushing on the next one. But you do impart some upward velocity on the particle during its brief time under your influence. This causes it to follow an upward path away from the point where you're pushing, which will continue until the circular path brings it back down. This will tilt the entire circle along the axis connecting the center of the circle to the point where you're pushing.

The faster the gyro spins, the less important the imparted velocity will be relative to the particle's speed, which is why a gyro is more stable the faster it spins.

Inertia is not a property intrinsic to an object but depends upon all the mass in the universe.

That quote from the article really crystallized Mach's Principle for me. So continuing mikeash's great explanation... basically the rest of the universe is pushing the gyroscope into its stable position?

But if so, we don't know how the universe does that, and relativity has failed to settle the matter so far. That's what I got from the article.

Don't rely much on Mach's Principle. It's a philosophical statement with exactly zero experimental evidence.

General Relativity would say somewhat the same thing, but in a very different form, with different results. GR would say that it depends on the geometry of the local spacetime, which, yes, does depend on all the mass in the universe, but not in the way that Mach's Principle would lead you to expect.

Note that GR, in contrast with Mach's Principle, does have experimental evidence.

This is a description of rotational stability, gyroscopic stability is: http://www.real-world-physics-problems.com/gyroscope-physics...

Key point

Gyroscopic stability also explains why a spinning axisymmetric projectile, such as a football, can have its symmetric (long) axis stay aligned with its flight trajectory, without tumbling end over end when in flight. The spin imparts a gyroscopic response to the aerodynamic forces acting on the projectile, which results in the projectile long axis aligning itself with the flight trajectory. The physics involved here is a combination of gyroscopic analysis and aerodynamic force analysis due to drag and (potentially) the Magnus effect. This is quite complicated and will not be discussed here. However, there is a lot of literature available online on gyroscope physics, as related to projectile spin and gyroscopic stability, if one wishes to study this topic further.

I once built a simple mass-spring physics engine, and this exact effect what was causing the wheels of my car-like mass-spring blob to bend "funny". It was only after I slowly debugged it (by removing friction, then gravity, softer springs, slower timescale etc) that I felt I really got how these forces come about.

I think the phrase "...which will continue until the circular path brings it back down" requires a bit more explanation. At this point, you seem to be switching from treating the rotating ring as a stream of independent particles to being a rigid body, but if you treat it as a rigid body from the start, the first part is no longer obvious.

I think that once you establish that angular momentum is a vector quantity that is entirely consistent with Newton's laws, then the particular case of the gyroscope becomes straightforward.

You can imagine each particle being somehow tethered to the center, without any need for the particles to be connected otherwise.

You’re totally right that gyroscopes are straightforward if you understand angular velocity as a vector quantity, but it’s not quite so intuitive.

If each particle is only tethered to the center, how does the circle bring it down again? If the tethers are all fixed to one another, we're back to rigidity.

Edit: I'm trying to think of a way to bring in angular momentum without having to derive it in full generality...

You could imagine that they’re connected to the center of rotation with a string or something. You just need centripetal force, not a rigid connection to anything. Although that may still be more than what you’re after....

string held taught by centripetal force is rigid. effect is the same.

a spinning disk 'averages' its mass distribution. Consider a gyroscope spinning fast. so if all of a sudden you try a push its top northward then that instantaneous force pushes down on the north edge of the disk and up on the south edge.Those specific parts of the disk acquire momentum. However because the disk is spinning, the part of the disk that was north soon becomes south. and the southern piece that was moving up is now north.now the momenta of the influenced disk segments act to right the gyroscope.

The same effect can occur during the acceleration of a gyroscope in a missile in space. Even tho there is no gravity. The effect of acceleration on the gyroscope is the same, causing it to maintain its orientation in space.

The faster a gyroscope spins, the more quickly it rights itself. and thus appears more stable. as it slows down, the righting effect fails.

Yes, though I think you can avoid the question of why just "those specific parts of the disk" by considering a dumbbell (two joined, point masses spinning around an axis perpendicular to the center of the rod joining them) rather than a disk or ring, and a continuous torque. If you are pushing northwards on the axis, the maximum rate of change of the instantaneous velocities of the point masses is when they are aligned north-south, and when they are aligned east-west, there is no change in their instantaneous velocity from the applied torque. Integrate this over one revolution, and you get the axis tipping in the east-west plane. A picture would really help, maybe I can find one on the web...

indeed it tips perpendicular to the direction of applied force. and this is what happens in reality. try spinning a bicycle wheel holding its axle on both ends. now try to twist the axle and it curiously wants to move the wheel in a perpendicular direction.

Um, I must be missing something here, because feel like I have a pretty simple solution to why there's only a single rotational reference frame, and this is a problem that apparently eluded Einstein, if I'm to believe your link.

Imagine a spinning glass ball with a 1cm radius doing one full rotation per second. If we draw a dot on its outer edge, at the end of 1 second that dot will have done a full turn. Given that its movement was a circle with radius 1, the distance the dot traveled was 2pi cm, for a speed of 2pi cm/s.

Now imagine that instead of drawing the dot on the outer edge, we drew it halfway between the center and the outer edge (somehow). This would place it 0.5cm from the center. It would still complete a full turn in 1 second, but now its distance traveled would be pi cm, for a speed of pi cm/s.

All this is to show that when the ball is spinning, the different particles it's composed of are moving at different speeds. On opposite sides of the ball, the particles are even moving in different directions. The faster the ball spins, the greater the difference in velocity of the different parts of the ball.

Rotation is inherently about different particles moving at different velocities. This is why there is an absolute reference frame for it: it is defined by these differences, so by reducing them to zero and making every particle in the ball have the same velocity, we can reach the "absolute".

At least, that's what it seems like to me.

That's an interesting idea.

Check out the second answer from 'Vesselin Petkov' which talks about a geometric case for the difference between the two. His answer overall seemed to me more interesting than the most upvoted one there.

Whoa. I kept reading past that, and the third answer by Logan R. Kearsley is almost exactly what I said, but better. I should have kept scrolling the first time I opened the link!

It ends by saying that in general relativity, "rotation can be considered as existing only relative to a certain choice of coordinates after all", though, so there seems to be more to it.

Is the particle in the centre moving at all?

Are the particles point mass?

I don't think a point can rotate. What would it mean if it did? There would be no observable change. So no, I don't think the absolute center point moves.

From a physical standpoint, though, if you wanted to talk about the absolute center point, you'd have to talk about the lowest level of particles, which gets into the weirdness of quantum mechanics (or maybe a lower level exists?). At that point, I really couldn't say what happens.

And I don't think it matters if the particles are point mass or not, except possibly for the absolute center. The point is that the rotating object is not just one thing, but made up of smaller things that have different velocities and acceleration. These differences in velocities and acceleration are what rotation is.

If there exists something that is not made up of smaller things which also rotates, then that would prove me wrong.

Of course, all the above is just speculation by someone who's hasn't had a physics class since high school, so take it with a grain of salt.

The most fundamental particle can't rotate, because that would imply that parts of it had different velocities from other parts... but it doesn't have parts at all, by initial definition. So, Democritus' atoms imply that rotation is not a fundamental motion.

I think every attempt to visualize this which imagines a single object rotating is doomed. Rotation inherently implies a difference in velocities, and some attractive force keeping those velocities changing to maintain a distance. So, the existence of any attractive force, together with inertia, implies rotation and the stickiness of direction of a gyroscope. But inertia itself already implied stickiness of direction, given that a change in direction would require acceleration...

Okay, then explain Spin. Angular momentum is defined by how a particle responds to fields, not by the relation of its parts.

I'm no physicist, of course. I had thought that 'spin' was metaphorical or analogous, like quarks' color and flavor, but Wikipedia asserts that it was originally considered to be rotation about an axis. So, I've no real clue. :)

We need a new "explain it like I'm 5" guide to modern physics. Or at least, "like I'm not a mathematician".

>Rotation is inherently about different particles moving at different velocities. This is why there is an absolute reference frame for it: it is defined by these differences, so by reducing them to zero and making every particle in the ball have the same velocity, we can reach the "absolute".

Imagine the ball is floating in space, and you are watching things through a camera fixed to the ball. To you, the two dots will always appear stationary with zero relative velocity. So there is no way to determine your absolute reference frame.

Now suppose you are watching through an external camera, and suppose you observe the dots having a relative velocity. Is the ball spinning, or is the camera orbiting around the ball? Again, there is no way to tell.

But if you were the camera you'd feel a force, or not, right? It's not like being in an elevator in free-fall, where you can't tell whether you're accelerating downwards or sitting still in flat space.

True, but the GP suggested that you can find the absolute reference frame by looking at the relative velocities of the dots (independent of any force measurements).

How would you tell whether that force is gravitational or centrifugal?

If it were gravitational there would have to be a mass in the right place to cause it. Maybe you could look at how the force changed as you moved around?

The elevator analogy breaks down if you're larger than a point-particle in a point-elevator. Gravity's force varies with distance, causing tidal forces on your body, allowing something large/sensitive enough to feel the difference. Gravity stretches you whereas uniform acceleration does not, and non-uniform acceleration compresses you.

In other words, you can determine that you're in a gravitational field by measuring the difference in force at different locations in the elevator.

>Certainly if you were alone in the universe, he thought, there would be no way to tell if you were rotating, so there could be no centrifugal force if you started to spin with respect to, say, another person.

Isn't that... intuitively wrong though? If you were spinning fast enough in space, your body would be ripped apart. If you were spinning and let go of an object near you, instead of floating in place, it would appear to retreat away from you rapidly.

I understand the example of how a person in a falling elevator can't tell if gravity is acting on them or not ... it's intuitive and there aren't any obvious contradictions. I don't get why these two examples are brought up together as similar obviously-true things that inspired relativity. It feels to me like it (the article / Mach / Einstein / physicists) is reaching for a parallel where there isn't one between cases that are only superficially similar.

Maybe the idea is that no other bodies around means that your own body would be uncontested in "frame-dragging" such to define that you aren't rotating? But what happens if you hold your arm out and throw a ball perpendicular to your arm? I can't imagine a type of rules of motion that would result in anything but your body being sent spinning slightly, with you seeing the ball retreat while appearing to orbit you and you being able to feel the blood rush a little more to the ends of your body away from the axis you're spinning on. The blood in your veins has inertia, and by changing the inertia of parts of your body, then of course you're going to get pushback from your blood. Maybe the ball being a separate body is now dragging the frame a bit such that you're now rotating relative to the frame, but if the ball has much less mass than you, it seems odd that the ball would have a great effect on the frame compared to you, and possibly continue to, no matter how far away it is from you. Every other effect at a distance rapidly diminishes with distance! This effect wouldn't be necessarily nonlocal (ie. faster than light), but it would seem to have a disrespect for distance not commonly found in physics. (Maybe the effect just diminishes outrageously slowly over distance, but I'm not sure this assails all of my concerns with the concept.)

I'd agree with your intuition in both cases, but it's worth pointing out the equivalence principle (falling in an elevator) isn't necessarily immediately obvious (which I know is not something you claimed). Feynman complained about philosophers who would claim it's obvious that motion was always relative but then wouldn't understand that the same thing didn't apply to rotational motion.

http://www.feynmanlectures.caltech.edu/I_16.html

Let me refine that part: I think that what would physically happen in the elevator example is apparent to most (someone with knowledge of Newtonian physics may agree with the idea that the interior of a falling elevator acts identically with the interior of an unmoving gravity-less elevator), but people without knowledge of relativity and the experiments that lead to it may disagree about what the elevator example means about physics and the world.

But the spinning-in-an-empty-universe example is a situation that I don't even agree with Mach/Einstein about what would happen, much less about what it says about the world. Maybe they're right, but this difference makes the thought experiment a much different kind and arguably a less compelling one than the other.

Thanks for the link, I found it an interesting read!

http://www.feynmanlectures.caltech.edu/I_20.html

There's also a lecture on inertial guidance in Feynman's tips on physics; it's more about the clever details of practical gyros.

Note that these explanations already presume rotation is absolute wrt an inertial frame.

My (undergraduate) understanding of the precession of the orbit of Mercury is that the longitude of the periapsis in Sun coordinates changes over time. The shape of the orbit stays the same, unless maybe it's changed a bit by perturbations from the outer planets.

Classically, you would expect the shape and position/rotation of the orbit to be constant. In reality, its rotation in the orbital plane changes due to GR.

Hmm, but if the perihelion changes position and the orbit doesn't change shape, the only other option is that the entire orbit shifts—is that it?

My understanding of precession is that there are two levels of rotation: an object rotating on some axis A, with axis A rotating around another axis B. So in the case of the perihelion precessing, what would be the corresponding parts? I was assuming the only precession taking place was of Mercury itself because the axis it rotates on (axis A) rotates about some other B axis.

Edit: to clarify, if the above is a correct description of precession, then in order for the perihelion itself to precess it would need to be rotating, and the axis it's rotating about would need to be rotating about another axis. My understanding is that neither the perihelion nor the orbit are rotating, so they can't be precessing.

"Precession" is just another word for rotation. It sounds like you're thinking of a spinning top, whose rotation axis will precess (rotate) around another axis (usually the local vertical).

In the context use here, the precession in question is the rotation of the perihelion (or, if you want to think of it more akin to the above case, the semimajor axis of the ellipse) that rotates in the orbital plane (around the normal vector to the orbital plane).

https://en.wikipedia.org/wiki/Apsidal_precession

Thanks, that article does clear it up. So the orbit doesn't change shape nor does it shift, instead it rotates (from the article: "More precisely, it is the gradual rotation of the line joining the apsides of an orbit"—so I guess the ellipse major axis rotates).

From what I can tell using precession as a direct substitute for rotation is less common, even in astronomy—but maybe I've just had poor samples so far. I was thinking of it as: "Precession is a change in the orientation of the rotational axis of a rotating body." (https://en.wikipedia.org/wiki/Precession)

its rotation in the orbital plane changes due to GR.

Actually, it would change even without GR. The orbital ellipse is only constant in the ideal two-body problem. The fact that planets aren't perfectly spherically symmetric, and the presence of the other planets, also cause the orbits to precess.

From the Wikipedia article I linked in my other post: "For Mercury, the perihelion precession rate due to general relativistic effects is 43″ per century. By comparison, the precession due to perturbations from the other planets in the Solar System is 532″ per century, whereas the oblateness of the Sun (quadrupole moment) causes a negligible contribution of 0.025″ per century."

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